Darius and Cyrus were names of Persian kings. In fact, there were several kings called Cyrus and Darius, but the ones relevant to the biblical record were
- Cyrus II (also known as Cyrus the great): 576–530 BC;
- Darius I (also known as Darius the great): 550–486BC.
Cyrus II is mentioned in the Bible in 2 Chronicles 36:22-23; Ezra 1:1-8; 3:7; 4:3-5; 5:13-17; 6:3,14; Isaiah 44:28;45:1; Daniel 1:21; 6:28; 10:1.
Darius I is mentioned in the Bible in Ezra 4:5,24; 5:5-7; 6:1-15; Nehemiah 12:22; Haggai 1:15; 2:10; Zechariah 1:1,7; 7:1.
Cyrus II and Darius I were both part of the Achaemenid family dynasty. Darius was the second cousin once removed of Cyrus II — Cyrus’s great grandfather Teispes was Darius’s great great grandfather. Darius was also Cyrus’s son-in-law as he married his daughter Atossa.
There is another Darius mentioned in Daniel 5:31; 6:1-28; 9:1; 11:1. He is known as “Darius the Mede” to distinguish him from the later King Darius I. We are told that he was about 62 years old when he became “king over Babylon” (Daniel 5:32). There are no other historical records of this Darius. Possibly he was the same person as Gobryas, a general of Cyrus I who helped conquer Babylon according to Xenophon.
For further discussion, see Gaston (2009) Historical issues in the book of Daniel.
You have Cyrus 576 – 530 while you have Darius 550 – 486. These seem to overlap. The Wikipedia article you link to has Darius starting at 522. Is that more correct?
Those dates are year of birth to year of death (as far as we know). Their lives overlapped. The years of reign were for Cyrus II from 559BC to his death, and for Darius I from 522 to his death.